I'm sure this has been asked before, but I wanted to know which A330 (both -200/-300) has the most range or fly the furthest. I reckon the A330-343X has the most range but I heard the A330-200 can fly the most.

The ACAP document referred to by Tdscanuck shows the current 233 tonne version of the A330-200 to be capable of 6 750Nm with a payload of around 25 tonnes.

LHR-NRT is 5 200Nm, at which still-air range the 233t A330-200 will lift about 90 000lb (about 41 tonnes, which is a pretty good payload)
Of course air is never still, so I'm guessing about 6 000Nm would be representative of real-world LHR-NRT, at which air range, the payload is around 75000lb or 34 tonnes.
That would equate to around 250 pax plus about 11 tonnes of cargo.
Which I guess means "yes"..

Since the ACAP was published, Trent powered A330's have reduced their SFC by 1.3% and P+W powered ones by around 1%. The Trent improvement should add c. 1 tonne to the payload capability at those ranges.

Of course, next year, airlines will be able to take A330-200's rated to 238 tonnes MTOW, which should make a very useful addition to the already useful range/payload capability that I've described.

Quoting Seemyseems (Thread starter):but I wanted to know which A330 (both -200/-300) has the most range or fly the furthest

The A330-300's are seriously fuel volume limited compared to the A330-200 without the A330-200's centre fuel tank.
As Tdscanuck said, the A330-200 gets within a whisker of MTOW just by filling the tanks - the 1.3% Trent 700 SFC gain should give the A330-200 a ferry range of the order of 9 500Nm - the same as the 748i